Sides of a triangle are in the ratio of 12 : | vedclass

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(D) Perimeter of the triangle $= 540 \, cm$.Semi-perimeter $s = \frac{540}{2} = 270 \, cm$.Let the sides be $12x, 17x,$ and $25x$.$12x + 17x + 25x = 5

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$9,000 \, cm^2$

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(D) Perimeter of the triangle $= 540 \, cm$.Semi-perimeter $s = \frac{540}{2} = 270 \, cm$.Let the sides be $12x, 17x,$ and $25x$.$12x + 17x + 25x = 540 \Rightarrow 54x = 540 \Rightarrow x = 10$.Thus,the sides are $a = 120 \, cm, b = 170 \, cm, c = 250 \, cm$.Using Heron's formula: Area $= \sqrt{s(s-a)(s-b)(s-c)}$.$s-a = 270 - 120 = 150 \, cm$.$s-b = 270 - 170 = 100 \, cm$.$s-c = 270 - 250 = 20 \, cm$.Area $= \sqrt{270 	imes 150 	imes 100 	imes 20} = \sqrt{81,000,000} = 9,000 \, cm^2$.

Sides of a triangle are in the ratio of $12 : 17 : 25$ and its perimeter is $540 \, cm$. Find its area.

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